Fundamentals of Mathematics in Medical Research: Theory and Cases is a comprehensive guide to the mathematical principles and methods used in medical research. This book is structured to facilitate learning and application and gives a solid foundation to readers. The book is divided into multiple parts that explain basic concepts in a progressive way. - Part I covers real-valued functions of one or more variables with geometric representations to establish a core understanding of advanced mathematics - Part II covers inferential methods of probability and statistics from basic probability to parametric and nonparametric tests - Part III covers correlation theory and advanced analysis of real-valued functions - Part IV covers multivariable analysis for solving complex problems with an explanation of Markov Chain models - An Appendix provides solutions for all exercises and along with Fortran 90 programs, Python scripts and Linux scripts to explore the mathematical concepts explained in the book. Key Features: Introduction and Conclusion in Every Chapter Exercises and Solutions Program codes and scripts Comprehensive Coverage of Mathematics for Academics and Research Real-World Cases This book is an essential resource for researchers, students, and professionals in medicine and allied fields who seek to understand and apply mathematical methods in their work.

Ordinary Differential Equations and Applications I: with Maple Examples blends the theory and practical applications of Ordinary Differential Equations (ODEs) with real-world examples, using Maple and MapleSim software. It covers fundamental ODE concepts, from first-order equations to more advanced topics like the Laplace and Mellin transforms, Fourier series, and power series solutions. The book includes detailed Maple examples demonstrating symbolic solutions, 2D and 3D plotting, and animated solution paths. Designed for undergraduate and postgraduate students in mathematics, physics, engineering, and other fields, it is also a valuable resource for professionals. The book addresses various applications in biology, economics, chemistry, and medicine. Key Features: - In-depth coverage of ODEs with real-world applications. - Maple examples for symbolic solutions, plotting, and animations. - Exploration of Laplace, Mellin, and Fourier series methods.

In The Generalized Relative Gol‘dberg Order and Type: Some Remarks on Functions of Complex Variables, the authors have discussed the generalized comparative growth analysis of entire functions of several complex variables at length. The discussion covers the important branch of complex analysis specially the theory of analytic functions of several variables. The book contains eight chapters. Chapter 1 presents introductory aspects of the topic and some preliminary definitions. In the proceeding chapters (2-8), the authors derive some results about the generalized Gol'dberg order (α,β) and generalized Gol'dberg type (α,β) of entire functions of several complex variables which progressively explores different variations of these variables, (upper and lower, functions, inequalities, growth measures). The book culminates in an explanation of the sum and product theorems depending on the generalized relative Gol'dberg order (α,β). This monograph is intended for mathematical researchers and enthusiasts who wish to expand their understanding about complex variables of several functions and complex and related aspects of complex analysis.

Mathematical Foundations of Time Series Analysis: Theory and Cases is designed for readers seeking depth and application alike, the book covers foundational ideas such as stationarity, decomposition, trend analysis, and autocorrelation, while also guiding readers through advanced tools like ARIMA models, Kalman filters, and wavelet-based forecasting. Organized into two distinct parts, the first section introduces the mathematical underpinnings of time series functions, including data behavior patterns, interpolation techniques, and multivariate models. The second section contextualizes these theories through real-world case analyses in areas such as financial risk, epidemiology, price indexing, and seismic activity. Each chapter incorporates examples, stepwise calculations, and remarks that reinforce both conceptual clarity and applied insight. Key Features: Defines and interprets the core components of time series, including trends, cycles, and seasonal patterns Models univariate and multivariate time-dependent data with precision Forecasts short-, medium-, and long-term events using advanced prediction frameworks Integrates statistical and computational tools for practical implementation Demonstrates applications of methodologies to diverse domains such as economics, health, seismology, and demographics Analyzes real datasets using worked examples and structured case-based reasoning